I converted my Trek FX from flat to drops. It was about $250-$300 in parts, and I didn't have to worry about hydraulic brakes. Your situation sounds more complicated. I'd second opinions about finding another bike if you're set on drops. In retrospect, I probably would have been better off getting a Trek 520 or Surly Long Haul Trucker.
I'm getting ready to swap my drops out for moustache bars, and someone suggested to me some Soma Sparrows, but they had a mount diameter of 22.2 and I needed 23.8 for my road levers, so I went with something different. But if you were open to moustache bars, the Soma Sparrow might work for you, and you wouldn't need to get new levers or shifters. Much cheaper, much easier.